Graphing Absolute Value Equations

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Graphing Absolute Value Equations

• How do I make one of those V graphs?

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Definition of Absolute Value

• x x if x gt 0
• 0 if x 0
• -x if x lt 0
• That way it is always positive or 0

• (x if positive)
• (0 if 0)
• (opposite of x if negative)

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What does the graph look like?

• V
• Minima lowest point of graph
• Vertex minima
• Sides are linear

• /\
• Maxima highest point of graph
• Vertex maxima
• Sides are linear

vertex
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Why is the graph a V?

• Y xthere are 2 values of x that will work for
  every y value. If x 3 and -3, y 3.
• There is only one y value that will only have one
  x value and that is called the vertex.
• The vertex is where the expression insdie the
  absolute value symbol is equal to zero

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How do I graph the Equation?

• X-coordinate of the vertex is the value of
• Plug in the value of x and solve for y
• This the ordered pair for the vertex
• (x,y)

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How do I graph the equation cont.

• Next, find x values to the left of the vertex and
  to the right of the vertex
• Solve for the y values

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How do I graph the equation cont.

• Lastly, plot the points and connect them forming
  a V or /\

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Example

• Find vertex x 1 0 x 1

vertex
(1, 2)
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Example
vertex

• Find x-coordinates to left and right, then
• solve for y- coordinate

(1, 2)
Left of vertex
Right of vertex
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Example

• Plot the points